Differential attacks are one of the main ways to attack block ciphers. Hence, we need to evaluate the security of a given block cipher against these attacks. One way to do so is to determine the minimal number of active S-boxes, and use this number along with the maximal differential probability of the S-box to determine the minimal probability of any differential characteristic. Thus, if one wants to build a new block cipher, one should try to maximize the minimal number of active Sboxes. On the other hand, the related-key security model is now quite important, hence, we also need to study the security of block ciphers in this model. In this work, we search how one could design a key schedule to maximize the number of active S-boxes in the related-key model. However, we also want this key schedule to be efficient, and therefore choose to only consider permutations. Our target is AES, and along with a few generic results about the best reachable bounds, we found a permutation to replace the original key schedule that reaches a minimal number of active S-boxes of 20 over 6 rounds, while no differential characteristic with a probability larger than 2 −128 exists. We also describe an algorithm which helped us to show that there is no permutation that can reach 18 or more active S-boxes in 5 rounds. Finally, we give several pairs (Ps, P k ), replacing respectively the ShiftRows operation and the key schedule of the AES, reaching a minimum of 21 active S-boxes over 6 rounds, while again, there is no differential characteristic with a probability larger than 2 −128 .
Division property is a cryptanalysis method that proves to be very efficient on block ciphers. Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property. Nonetheless, we claim that the previous techniques do not consider the full search space. We show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, we can potentially find a relevant distinguisher over a linearly equivalent function. We show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings. As a result, we exhibit a new distinguisher over 10 rounds of , while the previous best was over 9 rounds, and rule out such a distinguisher over more than 9 rounds of . We also give some insight about the construction of an S-box to strengthen a block cipher against our technique. We prove that using an S-box satisfying a certain criterion is optimal in term of resistance against classical division property. Accordingly, we exhibit stronger variants of and , improving the resistance against division property based distinguishers by 2 rounds.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.